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Question

If 1+2x+3x2+4x3+4, where |x|<1, then

A
least value of x is 12
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B
greatest value of x is 32
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C
least value of x is 23
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D
greatest value of x does not exists
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Solution

The correct option is D greatest value of x does not exists
S=1+2x+3x2+4x3+
xS=x+2x2+3x3+4x4+
(1x)S=1+x+x2+=11x
S=1(1x)2

Now, S4
1(1x)24
(x1)214
12x112
12x32
12x<1 ((0<|x|<1)

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